The answer is no, with an exception.
You cannot use two different cards in tandem for improved performance in-game to significantly increase fps through SLI or Crossfire technology. In order to take advantage of those technologies you need to use two cards with the same chipsets and clock speeds.
However, you can dedicate one card to handle demanding special effects, such as Nvidia Physx. (not sure what, or if there is an AMD equivalent of that though). This dedicated card does not need the same chipset and clock speed as your primary card. While not necessarily increasing overall performance, it allows you to turn on more "eye candy" without detriment to your performance.